The following are sample test questions from the National Assessment of Educational Progress for fourth-, eighth-, and twelfth-grade mathematics, with 11 questions for each grade placed in random order. Readers are invited to solve the problems and to try to guess the grade level that each question is designed to test. Click here for the answers.
These sample questions are taken from a list of more than 500 posted at http://nces.ed.gov/nationsreportcard/itmrls/itmrls.htm?MATLST .
1. Donna decides to buy a new car that is selling for $16,500. If she is required to pay 20 percent of the selling price as a down payment, what is the number of dollars required for the down payment?
A) $330
B) $1,650
C) $3,300
D) $4,125
E) $13,200
2. What is the length of this pencil to the nearest quarter inch?
[SHOW DIAGRAM D] A) 3-1/4 inches
B) 3-3/4 inches
C) 4-1/4 inches
D) 4 inches
E) I don’t know.
3. Mr. Garcia bought 5 dozen eggs at $0.89 per dozen. What was the total cost of the eggs?
A) $4.05
B) $4.45
C) $5.89
D) $10.68
4. A plumber charges a customer $48 for each hour worked plus an additional $9 for travel. If h represents the number of hours worked, which of the following expressions could be used to calculate the plumber’s total charge in dollars?
A) 48 + 9 + h
B) 48 x 9 x h
C) 48 + (9 x h)
D) (48 x 9 ) + h
E) (48 x h) + 9
5. Write two numbers that could be put in the [ ] to make the number sentence below true.
54 < 3 x [ ] Answer:____________________
6. Which of the following pieces of information would NOT be useful in deciding what type of car is the most economical to drive?
A) Median income of drivers
B) Range of insurance costs
C) Average miles per gallon
D) Typical cost of repairs per year
E) Cost of routine maintenance
7. On a flight from Los Angeles to New York, the cost of a fare was $400. Every seat was sold. What additional information do you need to find the total for all fares?
A) None
B) The number of employees on the plane
C) The number of passenger seats on the plane
D) The distance from Los Angeles to New York
8. Completely factor the polynomial 3x^2 – 14x – 5.
Answer: __________________
9. If the diameter of a circle is 30 centimeters, what is the radius of the circle?
A) 10 cm
B) 15 cm
C) 60 cm
D) 90 cm
E) 180 cm
10. A circle with diameter 10 centimeters is to be cut from a square of paper 10 centimeters on a side. Of the following, which is closest to the amount of paper left over after the circle is cut out?
A) 9 sq. cm.
B) 21 sq. cm.
C) 24 sq. cm.
D) 69 sq. cm.
E) 84 sq. cm.
11. Joe has 35 stamps in his collection. He buys 42 more. How many does he have in all?
A) 7
B) 35
C) 42
D) 77
E) 87
F) I don’t know.
12. What is the value of n + 5 when n = 3?
Answer: ____________________
13. Divide 15 into 30.45
Answer: ____________________
14. A measurement of 60 inches is equal to how many feet? (12 inches = 1 foot)
Answer: ______
15. Solve:
+5 + -5 = _______
16. Which is worth the most?
A) 35 pennies
B) 1 quarter
C) 4 dimes
D) I don’t know.
17. There is only one red marble in each of the bags shown below. Without looking, you are to pick a marble out of one of the bags. Which bag would give you the greatest chance of picking the red marble?
[SHOW DIAGRAM B] A) Bag with 10 marbles
B) Bag with 100 marbles
C) Bag with 1000 marbles
D) It makes no difference.
E) I don’t know.
18. N stands for the number of stamps John had. He gave 12 stamps to his sister. Which expression tells you how many stamps John has now?
A) N + 12
B) N – 12
C) 12 – N
D) 12 x N
19. Which of the following is true about 87% of 10?
A) It is greater than 10.
B) It is less than 10.
C) It is equal to 10.
D) Can’t tell.
E) I don’t know.
20. In right triangle ABC below, cos A =
[SHOW DIAGRAM H] A) 3/5
B) 3/4
C) 4/5
D) 4/3
E) 5/3
21. How many thirds are equal to one whole?
A) 1/3
B) 1
C) 2
D) 3
E) I don’t know.
22. Which number is between 1.2 and 1.3?
A) .123
B) .132
C) 1.23
D) 1.32
E) I don’t know.
23. The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work.
Answer: _______________
24. The weight of an object on the Moon is 1/6 the weight of that object on the Earth. An object that weighs 30 pounds on Earth would weigh how many pounds on the Moon?
Answer: ____________________
25. Subtract two three-digit numbers: 604 – 207
Answer: _______
26. Sam can purchase his lunch at school. Each day he wants to have juice that costs 50 cents, a sandwich that costs 90 cents and fruit that costs 35 cents. His mother has only $1.00 bills. What is the least number of $1.00 bills that his mother should give him so he will have enough money to buy lunch for 5 days?
Answer: _________
27. What is the PERIMETER of this rectangle?
[SHOW DIAGRAM E] A) 13 meters
B) 26 meters
C) 40 meters
D) 80 meters
E) I don’t know.
28. How many integers are there between SQUAREROOT(15) and SQUAREROOT(63)?
A) Three
B) Four
C) Five
D) Six
E) Seven
29. Anita is making bags of treats for her sister’s birthday party. She divides 65 pieces of candy equally among 15 bags so that each bag contains as many pieces as possible. How many pieces will she have left?
A) 33
B) 5
C) 4
D) 3
E) 0.33
30. Which of the following numbers, when rounded to the nearest thousand, becomes 27,000?
A) 26,099
B) 26,490
C) 27,381
D) 27,550
E) 27,640
31. Solve 184 divided by 115.
A) 0.625
B) 1.6
C) 1.625
D) 16
32. Write this number as a decimal:
3 3/10 = ________
33. Brett needs to cut a piece of string into four equal pieces without using a ruler or other measuring instrument. Write directions to tell Brett how to do this.
Answer: __________________________________________________________
